Cyclone Separator Challenge

OBJECTIVE:

1. To describe four empirical models that are used to calculate the efficiency of cyclone separator.

2. To perform an analysis on a given cyclone separator model by varying the particle diameter from 1 μm to and calculate the separation efficiency in each case.

3. To perform an analysis on a given cyclone separator model by varying the particle inlet velocity from 1 m/sec to 5 m/sec and calculate the separation efficiency and pressure drop in each case.

THEORY

Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators are one of many air pollution control devices known as pre-cleaners since they generally remove larger pieces of particulate matter.

Working & Principle

The high speed rotating (air)flow is established within a cylindrical or conical container called a cyclone. Air flows in a spiral pattern, beginning at the top (wide end) of the cyclone and ending at the bottom (narrow) end before exiting the cyclone in a straight stream through the center of the cyclone and out the top. Larger (denser) particles in the rotating stream have too much inertia to follow the tight curve of the stream and strike the outside wall, falling then to the bottom of the cyclone where they can be
removed. In a conical system, as the rotating flow moves towards the narrow end of the cyclone the rotational radius of the stream is reduced, separating smaller and smaller particles.

Applications:

General applications include:

oil refineries to separate oils and gases

cement industry

vacuum cleaners

An empirical model for cyclone separator efficiency.

IOZIA AND LEITH MODEL:

Iozia and Leith (1990) logistic model is a modified version of Barth (1956) model which is developed based on force balance. The model assumes that a particle carried by the vortex endures the influence of two forces: a centrifugal force Z, and flow resistance, W. Core length, zc, and core diameter dc, are given as

`z_c=(H-S)-[(H-S)/(D/B)-1][(d_c/b)-1]` for dc>B

zc=H−S fordc<B

(`d_c=0.47(((ab)/D^2)^-0.25 (D_e/D)^-1.4)`)

The addition made by Iozia and Leith on the original Barth (1956) model is the core length zc and slope parameter β expression which is derived based on the statistical analysis of experimental data of cyclone with D = 0.25 m. The collection efficiency ηi of particle diameter dpi can be calculated from

`n_i=1/(1+(d_(pc)/d_(p1))^beta)`

where, d_(pc)'is the 50% cut given by Barth (1956)

`d_(pc)=((9μQ)/(πPpzcV2max))^0.5`

2. LI AND WANG MODEL:

The Li and Wang (1989) model include particle bounce or re-entrainment and turbulent diffusion at the cyclone wall. A two-dimensional analytical expression of particle distribution in the cyclone is obtained. Li and Wang's model were developed based on the following assumptions:

1. The radial particle velocity and the radial concentration profile are not constant, for uncollected particles within the cyclones.
2. Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce re-entrainment on the cyclone wall are:

`c=ctheta` at `theta=0`

at θ=0">θ=0

`Dr((∂c)/(∂r))=(1−α)wc` at`R =D/2`

The tangential velocity is related to the radius of cyclone by:

`uR^n=constant`

The concentration distribution in a cyclone is given as:

`c(r,θ)=(c0(rw−rn)exp{λ[1k(1+n)r1+n]})/(∫_(rn)^(rw)exp{1K(1+n)r1+n}dr)`

where,

`k=((1−n)(ρp−ρg)d2Q)/(18μb(r^(1/w-(n))-r^(1/w-(n)))`

and

`lamda=((1-alpha)kw_w)/((D_i)(r_(w)^(alpha))`

The resultant expression of the collection efficiency is given as particle of our size is given as

`ηi=1−exp{−λθ1}`

where,

`θ1=2πS+L/alpha`

3. KOCH AND LICHT MODEL

Koch and Licht (1977) collection theory recognized the inherently turbulent nature of cyclones and the distribution of gas residence times within the cyclone. Koch and Licht

describe particle motion in the entry and collection regions with the additional following assumptions:

1. The tangential velocity of a particle is equal to the tangential velocity of the gas flow, i.e. there is no slip in the tangential direction between the particle and the gas.
2. The tangential velocity is related to the radius of cyclone by `uR^n ="constant"

A force balance and an equation on the particle collection yields the grade efficiency ηi

`ηi=1−exp{−2[GτiQ/(D3)(n+1)]^(0.5n+1}`

where

`G=(8kc)/(k^2ak^2b)`

`n=1−{1−(12D)^0.14/2.5}{T+460/530}^0.3`

`τi=(ρ_pd_(p_i)^2)/(18μ)`

G is a factor related to the configuration of the cyclone, n is related to the vortex and τ is the relaxation term.

4. LAPPLE MODEL

Lapple (1951) model was developed based on force balance without considering the flow resistance. Lapple assumed that a particle entering the cyclone is evenly distributed across the inlet opening. The particle that travels from inlet half-width to the wall in the cyclone is collected with 50% efficiency. The semi-empirical relationship developed by Lapple (1951) to
calculate a 50% cut diameter, dpc">dpc is

`n_i=1/(1+(d_(pc)+bar(d_(p i)))^2`

`dpc=[(9μb)/(2πN_(nc)v_i(ρ_p−ρ_g)]12]`

where `N_c`is the number of revolutions

`N_c=1/a[h+(H−h)/2]`

PART 2: Analysis of cyclone separator model by varying particle size and to calculate the separate efficiency

Geometry

The geometry is imported into the SpaceClaim and do we analyze the physics inside the device we extract the fluid volume

Then we suppress for physics to avoid any interruption.

Mesh

Element size:10mm

No of Nodes:22951

No of Elements:112565

Solver

Physics Pressure Based

Solve: Pressure Based

Time: Steady-state

Velocity Formulation: Absolute

Gravity:-9.8m/s long y-direction

Viscous Model:k Epsisolon-->RNG model Swirl Dominated Flow

Discrete Phase Modelling

As

Here solid particles ranging from 1upn to 10 upm are simulated as a discrete phase in a continuum

• Enable interaction with continuous phase
• Enabled update DPM source every flow iteration
• Tracking parameter No of steps:50000

Click on Injections right at the bottom

• Injection Types: Surface
• Release from Surface: inlet
• Particle Types: Inert
• Material Type: Anthracite
• Diameter:Varying from 1e-6 to 10e-6
• Velocity :3 m.sec along x-direction
• Flow Rate:1e-20kg/s

Boundary Conditions

Inlet: velocity 3m/sec,DPM:Reflect

Outlet top :0Pa,DPM:Escape

Outlet bottom :0Pa,DPM:Trap

In addition to these setting, some other parameters are setup making changes in Solution Method

Pressure Velocity coupling

Scheme: Simple

Under Spacial Discretization

• Gradient: Least Square Cell-Based
• Pressure: Second Order
• Momentum: Second-Order Upwind
• Turbulent Kinetic Energy: First Order Upwind
• Turbulent Dissipation Rate: First Order Upwind

Initialization

Standard--Compute from the inlet

Run Calculation:700iteration

Case I: Particle Size 1e-6

Vortex Region

Separation Efficiency = No of Particles Trapped/No of Particle Tracked x 100

Separation Efficiency = 30/124 x 100=24%

case I : Particle Size 4e-6

Vortex Region

Seperation Efficiency = No of Particles Trapped/No of Particle Tracked x 100

Seperation Efficiency = 112/124 x 100=90.3%

Case III : Particle Size 7e-6

Vortex Region

Seperation Efficiency = No of Particles Trapped/No of Particle Tracked x 100

Seperation Efficiency = 122/124 x 100=98.38%

Case I : Particle Size 10e-6

Vortex Region

Separation Efficiency = No of Particles Trapped/No of Particle Tracked x 100

Separation Efficiency = 123/124 x 100=99.19%

CASES	Fluid particle size	Particle Tacked	Particle trapped	Particle Escape	Separation Efficiency
I	1μpm	124	30	33	24
II	4μpm	124	112	11	90.3
III	7μpm	124	122	1	98.38
IV	10μpm	124	123	0	99.19

Part 3

The geometry, Mesh and Setup are similar to the above the only change needed is varying the inlet velocity

• DPM>>INJECTION
• Release from Surface: inlet
• Particle Types: Inert
• X velocity: Varying from 1 m./sec to 5m/sec

Boundary Condition

Inlet Velocity: Varying from 1 m./sec to 5m/sec

Case I:1m/sec particle velocity

Inlet Total Pressure

Outlet Up Total Pressure

Pressure Contour

Vortex Region

Case II:3m/sec particle velocity particle velocity

Inlet Total Pressure

Outlet Up Total Pressure

Pressure Contour

Vortex Region

Case Iii:5m/sec particle velocity

Inlet Total Pressure

Outlet Up Total Pressure

Pressure Contour

Vortex Region

Cases	Particle Velocity	Particles Tracked	Particle trapped	Particle Escaped	Separation Efficiency	Pressure Inlet	Pressure Outlet TOP	Pressure DRop
I	1m/s	124	9	1	7.2%	0.25	2.19	1.94
II	3m/s	124	119	4	95.9%	2.7	19.49	2.7
III	5m/s	124	122	2	98.3%	7.94	55.462	47.522

Conclusion:

1. From the first table, it can be said that the with the increment in the size of the particle the no particle trapped will also increase and so is the separation efficiency

2. Separation efficiency in terms of particles velocity shows a proportional result ie rise in efficiency with an increase in velocity

3. The simulation also displays that with higher velocity the pressure drop is also high